Let's begin by mapping out some context by assuming the following goals of implementing QE:

prevent dire systemic liquidity concerns

reach inflation targets

manage expectations in the private sector

If I'm not mistaken, the vast majority of QE has been government debt securities. However, in principle, any asset class could be bought under by issuing central bank liabilities.

Question

If my understanding is correct that any asset class can be bought by issuing a liability (central bank money), then why have we only seen government debt securities be purchased historically? Would a broader range of asset purchases not help the Fed with the goals of QE as listed in the above bullet points?